Vincent, Billy and Zeph had some marbles in the ratio of 5 : 6 : 11. Zeph gave 50% of his marbles to Vincent and Billy. As a result, Vincent had the same number of marbles as Billy and Zeph had 11 fewer marbles than Vincent.

1. What was the percentage increase in Vincent's marbles after receiving from Zeph?
2. How many marbles did Billy have at first?

Vincent	Billy	Zeph	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of marbles that Zeph gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of marbles that Vincent and Billy each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of marbles that Vincent had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Vincent's marbles after receiving from Zeph
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 11
8.25 u - 5.5 u = 11
2.75 u = 11

1 u = 11 ÷ 2.75 = 4

Number of marbles that Billy had at first
= 6 u
= 6 x 4
= 24

Answer(s): (a) 65%; (b) 24